Abstract:

 

I present recent work of our group on realizing computational complexity in conformal field theories in view of relating it holographically to complexity proposals in AdS gravity. Gates and cost functions in the CFT are introduced and used for a complexity definition based on geometric actions on Virasoro and Kac-Moody orbits. We discuss a relation to the Euler-Arnold approach in Hamiltonian dynamics. In a complementary project, we developed a new method for evaluating modular flows for 1+1-dimensional chiral fermions, working directly from the resolvent in complex analysis. Both projects provide new ingredients for exploring the connection between spacetime and entanglement.

Talk based on 2004.03619 and 2008.07532